A Topological Picturebook by George K. Francis

By George K. Francis

Praise for George Francis's A Topological Picturebook:

Bravo to Springer for reissuing this targeted and lovely e-book! It not just reminds the older new release of the pleasures of doing arithmetic through hand, but in addition exhibits the recent iteration what ``hands on'' relatively means.

- John Stillwell, college of San Francisco

The Topological Picturebook has taught an entire new release of mathematicians to attract, to work out, and to think.

- Tony Robbin, artist and writer of Shadows of truth: The Fourth measurement in Relativity, Cubism, and sleek Thought

The vintage reference for a way to offer topological details visually, filled with remarkable hand-drawn photographs of complex surfaces.

- John Sullivan, Technische Universitat Berlin

A Topological Picturebook shall we scholars see topology because the unique discoverers conceived it: concrete and visible, freed from the formalism that burdens traditional textbooks.

- Jeffrey Weeks, writer of The form of Space

A Topological Picturebook is a visible banquet for someone occupied with mathematical photographs. Francis offers beautiful examples to construct one's "visualization muscles". even as, he explains the underlying ideas and layout innovations for readers to create their very own lucid drawings.

- George W. Hart, Stony Brook University

In this selection of narrative gem stones and interesting hand-drawn images, George Francis demonstrates the chicken-and-egg dating, in arithmetic, of photo and textual content. because the ebook used to be first released, the case for images in arithmetic has been gained, and now it's time to contemplate their that means. A Topological Picturebook continues to be indispensable.

- Marjorie Senechal, Smith university and co-editor of the Mathematical Intelligencer

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Example text

Labeled E, with its equatorial circle as B and a crosscut for F, this becomes a good pictograph for a nontrivial fiber bundle. In the second instance, a working figure is part of the exposition, and substitutes for a cumbersome, set-theoretic description of a topological procedure. Current taste in mathematical rigor prefers text which dispenses with pictures. A good working figure is useful for composing such rhetoric and keeping track of its logic. Because detail is added piecemeal to a working figure, graphical accuracy and visual clarity are essential here.

Beyond this, the sky is the limit and art supply stores are a good source of liberal advice on advanced tools such as lettering guides, pencil sharpeners, electric erasers and the like. Reduction of up to 50 percent produces flattering prints. For this reason I generally use a size 0 or I pen for ordinary lines, 2 or 3 for borders and lettering, 00 or 000 for shading and construction lines, all with fairly good results. CHALK AND BLACKBOARD. Yuri Rainich, who first introduced me to the wonders of projective geometry, held that the presence of rotations in the Euclidean group of congruences reflects the Greek habit of drawing figures on the ground as the students stood about in a circle.

Since the solvent of many inks will smear adjacent pigments already applied, I sometimes color on alternating sides of the sheet. When using several overlays, it pays to tape the sheets together, so that they fit correctly. COMPUTER AND DRAFfING TABLE. Computer-generated visual displays certainly are marvelous aids to the imagination. This spectacular new medium has been used by Tom Banchoff [1977] and Nelson Max [1977] to produce films of great beauty and lucidity in geometry and topology, respectively.

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